Let $a$ and $b$ be two reals satisfying $a < b$. Show that $\forall \lambda \in [0,1], \mathrm{e}^{\lambda a+(1-\lambda) b} \leqslant \lambda \mathrm{e}^{a}+(1-\lambda) \mathrm{e}^{b}$.
Let $a$ and $b$ be two reals satisfying $a < b$. Show that $\forall \lambda \in [0,1], \mathrm{e}^{\lambda a+(1-\lambda) b} \leqslant \lambda \mathrm{e}^{a}+(1-\lambda) \mathrm{e}^{b}$.